x^4-x^2-720=0

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Solution for x^4-x^2-720=0 equation: 


Simplifying
x4 + -1x2 + -720 = 0

Reorder the terms:
-720 + -1x2 + x4 = 0

Solving
-720 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '720' to each side of the equation.
-720 + -1x2 + 720 + x4 = 0 + 720

Reorder the terms:
-720 + 720 + -1x2 + x4 = 0 + 720

Combine like terms: -720 + 720 = 0
0 + -1x2 + x4 = 0 + 720
-1x2 + x4 = 0 + 720

Combine like terms: 0 + 720 = 720
-1x2 + x4 = 720

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = 720 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 720 + 0.25

Combine like terms: 720 + 0.25 = 720.25
0.25 + -1x2 + x4 = 720.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 720.25

Calculate the square root of the right side: 26.837473801

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 26.837473801 and -26.837473801.


Subproblem 1
x2 + -0.5 = 26.837473801

Simplifying
x2 + -0.5 = 26.837473801

Reorder the terms:
-0.5 + x2 = 26.837473801

Solving
-0.5 + x2 = 26.837473801

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 26.837473801 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 26.837473801 + 0.5
x2 = 26.837473801 + 0.5

Combine like terms: 26.837473801 + 0.5 = 27.337473801
x2 = 27.337473801

Simplifying
x2 = 27.337473801

Take the square root of each side:
x = {-5.228525012, 5.228525012}


Subproblem 2
x2 + -0.5 = -26.837473801

Simplifying
x2 + -0.5 = -26.837473801

Reorder the terms:
-0.5 + x2 = -26.837473801

Solving
-0.5 + x2 = -26.837473801

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -26.837473801 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -26.837473801 + 0.5
x2 = -26.837473801 + 0.5

Combine like terms: -26.837473801 + 0.5 = -26.337473801
x2 = -26.337473801

Simplifying
x2 = -26.337473801

Reorder the terms:
26.337473801 + x2 = -26.337473801 + 26.337473801

Combine like terms: -26.337473801 + 26.337473801 = 0.000000000
26.337473801 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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